Hello Yokamayokama and welcome to Writefix!

Overall, organization is evident. With an opinion in the intro and two paragraphs giving examples to support your opinion. A third body paragraph does mention the other side, and then repeats your opinion. The conclusion gives your opinion again. The essay is 314 words long which is OK, but it has very long sentences. You should aim at reducing the average length of your sentences by

• Adding some short sentences
• Breaking up longer sentences
• Making sure sentences have one idea

Intro

You wrote in your first sentence

I do not agree with this opinion to a larger extent.

Don’t begin like this, with a reference to question. Imagine if someone came up to you in the street and said “I completely agree with you.”  You would walk away quickly!

In an essay, you must start from the beginning -  no “I disagree with this” or “This statement is wrong.”  Remove the pronouns and specify.Here's one possible rewrite:

I don’t agree with limiting grants to science research. 

Usage

• Researches → research (research is ALWAYS non-count -  it doesn’t have a plural)
• Due to the progression of technology, people nowadays can lead a convenient and comfortable life.→Thanks to technology, people lead comfortable lives.
• With no doubt, the emergences of television, computer, and mobile phone are all to attribute to scientific research → emergence, attributed to.... 

Let's rewrite this whole sentence:

• Science gave us television, computers, and mobile phones. OR
• Scientific research gave us television, computers, and mobile phones.

• it is by no means pointless that → governments have a responsibility to fund many areas of research (avoid double negatives)
• Some departments…are deserved the subsidy from government → some departments deserve government subsidies
• It is hardly to image how society could function → It is hard to imagine

…when one day government stops allocating money to common subject research→ (Verb tense  -  this should be a conditional)

It is hardly to image how society could function well when one day government stops allocating money to common subject research. (21 words)

Let’s shorten it as well:

What would happen if governments stopped funding much research? (9 words)

• In my essay, I will look at the significance of studying less useful subjects and outline my analysis  (These words do not add to your sentence and do not help the reader to guess what is coming.)

People can get to know their predecessor’s custom and culture, as well as understanding the history of mankind’s development via studying the ancient literature →

People can learn their culture and customs and appreciate the history of mankind’s development by studying ancient literature.

Long sentences

Shorter, shorten, shorten: Do your best to have at most 20-25 words per sentence. This monster is 36 words long.

Also, research on linguistics, for example, is likely to raise people’s awareness of preserving their native languages, helping to slow down the speed of the extinction of lesser-known languages, which is beneficial to cultural identities. (35 words)

Here's a rewrite

Studying linguistics can preserve lesser known languages and increase cultural awareness. (11 words)

Another one with some unnecessary words:

By saying that, I mean some departments, which focus on finding solutions for unemployment issue and reducing crime rate, are deserved the subsidy from government.

Here's a shorter version:

We need more, not less, research to solve unemployment or reduce crime rates.

Lets shorten this sentence

Rather than hearing the exciting news of advanced robots and missiles, I believe the majority are more willing to see that their social security is ensured.

Yes, it has ‘only’ 26 words, but it has a misplaced modifier (rather+I) and a wrong word choice (‘exciting’).

Most people would prefer money spent on social security than on robots and missiles. 
OR

I believe most people would rather see money spent on their social security than on scientists’ pet projects of robots and missiles. (22 words)

Some of your sentences are not particularly long, but they are very heavy. Try to use fewer nouns and to replace them with verbs. This will make your writing flow. Here's a very heavy one:

In addition, funding economic subjects is indispensable. Without adequate financial support, economists would not devote themselves to resolving economic recession, which could pose a threat to the economic stability. (29 words)

• Without funding, economists cannot find answers to financial crises. (11 words) OR
• Without funding, we would not have economists to advise us on financial problems. (13 words) OR
• Funding research in economics could help us find our way out of recession. (13 words)

 I’m also not very satisfied with the word choice of ‘departments’  -  research can take place in many places outside universities:

• If we want to lower unemployment and to reduce crime, we need to provide funds for research in these areas. (20 words) OR
• Research on social areas such as labor and crime can reduce unemployment and lower crime. (15 words)

This long sentence has a fragment. It needs to be broken up.  There is also a problem with word order/usage (‘even it has to be conceded’). There is another double-negative here, and a passive. Why so complicated? Simplify!

But even it has to be conceded that scientific research is crucial, there is no getting around the fact that non-scientific subjects should not be ignored.  (26 words, fragment, usage, passive, double-negative)

Here's one rewrite:

While funding for physics, chemistry, biology or other ‘hard’ sciences is crucial, we cannot ignore research in other areas. (20 words )

Phew!

Overall, yokamayokama, there is no benefit to be gained from writing elaborately-structured complex sentences unless they are absolutely correct. Just be simple. A rule of thumb is to write for your younger niece or brother. If they can read it easily, you have met the IELTS requirement. Really! 

Hi Yokama

It's a very good question! What does heavy mean?

It's not really a formal description: it's my own term. Here's a 'heavy' sentence

From the start of the human society, the necessity of cure for sickness has been significant.

There are six nouns (human, society, necessity, cure, sickness, start, human society) and only one verb (the verb 'to be').

(I'm using a liberal definition of the word noun)

Here's the same sentence with fewer nouns

We have always needed doctors.

Two nouns: 'we' and 'doctors', and a slightly more interesting verb, 'needed'

There's a good post here about what they call nominalizations, or, in simpler words, nouns!

They give some good examples:

Candidate marking standards processes must experience improvement.(six sort-of-nouns, one verb)

We need to improve how we mark. (One noun, two verbs)

Here's another webpage about nominalizations:

"The commencement of the ceremony will be at noon.”

The ceremony will start at noon.

I will look for more examples of sentences which are 'heavy' with nouns, now that I know that they should be called nominalizations!